基于高层次结构数据的多水平模型贝叶斯推断及应用

面对具有多层次嵌套结构的数据,构建多水平模型是统计建模的一个重要研究课题。经典的参数估计方法主要采用极大似然估计法(ML),然而当面对高层数量单位小或数据结构不平衡时,极大似然估计在估计精度上存在一定不足;而贝叶斯方法充分应用了有效的先验信息,可以弥补其不足。本文在高层次结构数据多水平模型的研究基础上,探索高层次结构数据的多水平模型贝叶斯推断理论,并以云南省红河州农户收入数据作实证分析,建立了基于县-村-户嵌套结构的农户收入影响因素多水平模型,对比分析模型参数的ML估计、经验贝叶斯(EB-ML)估计和完全贝叶斯估计,从而充分展现了高层次结构数据多水平模型的完全贝叶斯推断方法,在拟合高层数量单位小或数据不平衡时具有的特征和优势。     

实证因子模型的贝叶斯半参数分析和模型比较（英文）

为了解决多元数据的异质性,对因子分析模型建立了贝叶斯半参数程序.方法依赖于有限混合分布空间上先验分布的使用.分块吉布斯抽样器用以进行后验分析.L_v测度和贝叶斯因子给出模型比较.基于广义加权中国餐馆算法,给出了半参数模型下数据似然的计算.经验结果显示了方法的有效性.     

基于贝叶斯网络的工程项目进度完工概率分析

针对传统计划评审技术(Program Evaluation and Review Technique,PERT)在计算完工概率时假设条件的局限性(假设条件与工程实际存在偏差,导致完工概率偏大),提出了基于贝叶斯网络的施工进度完工概率分析方法.首先,分析了贝叶斯网络与进度计划网络之间的相似性,将两者结合起来构建了贝叶斯进度网络;在此基础上,综合考虑贝叶斯网络在节点取值及概率计算方面的优越性,并结合工程项目的不确定性及复杂性特点,建立了基于贝叶斯网络的施工进度完工概率分析模型.最后,将该模型应用于具体工程进行实例分析,验证了模型的可行性与有效性.研究结果表明:基于贝叶斯网络的进度完工概率模型充分考虑了工程施工中的风险因素,其结果能更客观地反映工程实际,可为工程项目决策者提供可靠的依据.     

基于粒度计算的探索性分析建模研究

从现有探索性分析模型建模方式的局限性出发,提出了探索性分析模型的粒度原理,建立了基于粒度计算的探索性分析模型,给出了该模型的因素集粒化、因素水平值域粒化以及混合粒化三种粒度获取方式,针对探索性分析模型的追溯问题,分析并建立了粒度空间各层次间的层级关联映射和软构层映射.在此基础上,能够建立探索性分析模型的一般性数学描述.     

贝叶斯分类模型的改进及其应用

利用加权贝叶斯分类模型对北京科技大学本科生英语四级考试通过率进行预测.通过对误判数据的分析,调整贝叶斯分类器的判别条件,改进了加权贝叶斯分类模型.实验表明,改进后的模型大大提高了预测结果的准确性.此外,还引入了学生"潜力因子"的概念,为教学与学习提供了个性化的提示和有针对性的建议.     

基于系统冲击的灰色预测模型及其应用研究

针对系统受到系统外部冲击问题,结合泛函理论和灰色系统理论,建立了含有系统冲击泛函分析因子的灰色泛函预测模型。并运用贝叶斯网络推理技术,建立了系统冲击与系统控制的灰色贝叶斯网络推理预测模型。所建模型可以分析基于系统冲击演化的泛函分析因子的动态推演问题。依据泛函分析因子的变动,可以预测与修正系统发展趋势。案例分析了2013年房地产经济受到新政策的冲击问题。由于房地产经济受到新政策冲击,使经济发展态势发生转变。根据房地产经济的当前时段信息,利用灰色贝叶斯网络推理预测模型对历史趋势进行修正,预测结果与实际数值仅有3.81%的偏离,预测结果较其它现有模型的预测结果精确。灰色贝叶斯网络推理模型强调对近期数据的开发利用,适用于预测系统近期受到外部冲击的发展趋势问题。     

地震灾害人员伤亡预测模型研究

地震人员伤亡的准确预测和评估是开展应急准备的重要前提,也是震后快速响应的重要依据.对典型的地震人员伤亡预测模型进行了总结和比较,探讨了各类模型的适用特性,搜集了云南省1996-2015年历史地震案例数据,利用相关性分析提取了影响人员伤亡的主要因素,通过对多元归回模型添加二次项并进行对数变换修正,建立了地震灾害伤亡人员预测模型,并通过案例应用验证了模型的有效性.     

利用贝叶斯网络分析基因表达数据

利用基因表达数据提出一种新的网络模型—贝叶斯网络,发现基因的互作.一个贝叶斯网络是多变量联合概率分布的有向图模型,表示变量间的条件独立属性.首先我们阐明贝叶斯网络如何表示基因间的互作,然后介绍从基因芯片数据学习贝叶斯网络的方法.     

商业建筑人员疏散系统模型的构建与决策

针对我国商业建筑火灾事故频发、群死群伤事故严重的现状,对全国商业建筑特大火灾案例进行统计调查,建立人员疏散系统模型数据采用贝叶斯统计分析方法进行分析,克服了火灾数据缺乏、且难以进行大量重复实验的困难,得到各基本事件发生概率的条件期望估计与方差.通过误差传播对系统进行敏感性分析.通过对系统故障树的分析,得到在火灾发生情况下商业建筑人员疏散失败的概率及方差,并进行系统决策.     

艾滋病防治资源投入的效果分析

基于GOALS模型的基本思想,建立了效果分析模型,并针对两种不同的资金分配方案,模拟了两种方案对2006—2010年某地艾滋病流行的影响,并对模拟结果进行了分析.     

Vague集上模糊熵的几点注记

V ague集上的不确定性度量有两种途径,一种是度量V ague集是模糊集的程度,一种是度量V ague集具有的模糊性的程度。后者将模糊集的模糊熵作为特例。本文基于“投票模型”分析了V ague集的熵应具有的特征,对国内作者提出的V ague集上的模糊熵进行了评述。     

GM(1,1)模型的改进及其在银行贷款预测中的应用

利用GM(1,1)预测模型,分析中国近年来信贷变化,发现中国信贷规模发展趋势及其信贷结构具有显著的新特征;结合模型的适用条件和预测结果的检验要求,提出了四条思路解决数据缺损导致信息挖掘失真以及如何处理数据中所包含的大量"噪音"等问题,并认为对那些波动较大的数据应采取连续平滑的方法改造原始数据;对于那些有奇异值的原始数据可采用插值法替代它,试验和案例应用印证了改进的模型可以提高预测精度.     

Likelihood robust optimization for data-driven problems

We consider optimal decision-making problems in an uncertain environment. In particular, we consider the case in which the distribution of the input is unknown, yet there is some historical data drawn from the distribution. In this paper, we propose a new type of distributionally robust optimization model called the likelihood robust optimization (LRO) model for this class of problems. In contrast to previous work on distributionally robust optimization that focuses on certain parameters (e.g., mean, variance, etc.) of the input distribution, we exploit the historical data and define the accessible distribution set to contain only those distributions that make the observed data achieve a certain level of likelihood. Then we formulate the targeting problem as one of optimizing the expected value of the objective function under the worst-case distribution in that set. Our model avoids the over-conservativeness of some prior robust approaches by ruling out unrealistic distributions while maintaining robustness of the solution for any statistically likely outcomes. We present statistical analyses of our model using Bayesian statistics and empirical likelihood theory. Specifically, we prove the asymptotic behavior of our distribution set and establish the relationship between our model and other distributionally robust models. To test the performance of our model, we apply it to the newsvendor problem and the portfolio selection problem. The test results show that the solutions of our model indeed have desirable performance.     

基于结论一致的综合评价数据标准化研究

主要分析了数据标准化方法对综合评价加权求和法结论的影响;发现数据标准化方法对评价结论的影响主要体现在两个方面,一是使某些属性值无法参与计算,一是改变了属性间恒定的相互置换率;通过设定满足一定比例要求的理想解,可以消除数据标准化方法对加权和法评价结论的影响,获得一致的评价结论.     

Simplifying essential competencies for Taiwan civil servants using the rough set approach

Applying competency models to identify and develop capabilities of civil servants is now a leading strategy for every government. However, an ideal competency model usually contains too many intended competencies, impeding implementation. Recently, some scholars and experts argued that there is a maximum of eight competencies for effective assessment. Hence, how to simplify a set of competencies becomes an important issue. This study is presented as a test case to extend practical applications of rough set theory (RST) in the human resource field of Government. A well-known data mining technique, RST is a relatively new approach to this problem and is good at data reduction in qualitative analysis. Hence, the rough set approach is suitable for dealing with the qualitative problem in simplifying a set of competencies. This paper slimmed a set of competencies using RST, thus helping the Taiwan Government to better understand the perceived competency levels of its civil servants. Using the rough set analysis, this paper successfully reduced the numerous essential competencies into a more compact set, by omitting low-consensus competencies.     

集值均衡问题近似Benson真有效解的非线性刻画

在一般的数学模型中,由于要忽略一些次要因素,所建的模型往往是近似的,且对数学模型利用数值算法所求得的解大多是近似解。另一方面,在可行集非紧的情况下,精确解的解集往往是空集,而在较弱的条件下近似解集可以是非空的。在Hausdorff局部凸拓扑线性空间中分别研究了无约束和带约束集值均衡问题近似Benson真有效解。在没有任何凸性假设下,利用非线性泛函分别建立了最优性条件。     

Approximate Bayesian shrinkage estimation

A Bayesian shrinkage estimate for the mean in the generalized linear empirical Bayes model is proposed. The posterior mean under the empirical Bayes model has a shrinkage pattern. The shrinkage factor is estimated by using a Bayesian method with the regression coefficients to be fixed at the maximum extended quasi-likelihood estimates. This approach develops a Bayesian shrinkage estimate of the mean which is numerically quite tractable. The method is illustrated with a data set, and the estimate is compared with an earlier one based on an empirical Bayes method. In a special case of the homogeneous model with exchangeable priors, the performance of the Bayesian estimate is illustrated by computer simulations. The simulation result shows as improvement of the Bayesian estimate over the empirical Bayes estimate in some situations.     

A classification model based on goal programming with non-standard preference functions with application to the prediction of cinema-going behaviour

This paper presents a goal programming model that allows for the flexible handling of the two group classification problem. The goal programming model is based around the concepts of non-standard preference functions and penalty function modelling. An extension to a generalised distance metric case is given. The inclusion of multiple levels of classification based upon different levels of certainty is incorporated into the model. The model is tested on a real-life data set pertaining to cinema-going attendance and conclusions are drawn both in the context of the methodology and of the application.     

An axiomatic approach to scalar data interpolation on surfaces

We discuss possible algorithms for interpolating data given on a set of curves in a surface of ℝ³. We propose a set of basic assumptions to be satisfied by the interpolation algorithms which lead to a set of models in terms of possibly degenerate elliptic partial differential equations. The Absolutely Minimizing Lipschitz Extension model (AMLE) is singled out and studied in more detail. We study the correctness of our numerical approach and we show experiments illustrating the interpolation of data on some simple test surfaces like the sphere and the torus.     

Fuzzy confidence interval for pH titration curve

In this paper we present a new method of confidence interval identification for Takagi–Sugeno fuzzy models in the case of the data with regionally changeable variance. The method combines a fuzzy identification methodology with some ideas from applied statistics. The idea is to find, on a finite set of measured data, the confidence interval defined by the lower and upper bounds. The confidence interval which defines the band that contains the measurement values with certain confidence. The method can be used when describing a family of uncertain nonlinear functions or when the systems with uncertain physical parameters are observed. In our example the proposed method is applied to model the pH-titration curve.